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Anke has 5 fewer candies than Conrad. If Anke gives Conrad 5
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14 Jun 2018, 14:25
14 Jun 2018, 14:25
Expert Reply
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Question Stats:
74% (01:41) correct
25% (02:12) wrong based on 51 sessions
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Anke has 5 fewer candies than Conrad. If Anke gives Conrad 5 candies, Conrad will then have 4 times as many candies as Anke. How many candies does Anke have?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Re: Anke has 5 fewer candies than Conrad. If Anke gives Conrad 5
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02 Jul 2018, 22:16
02 Jul 2018, 22:16
1
sandy wrote:
Anke has 5 fewer candies than Conrad. If Anke gives Conrad 5 candies, Conrad will then have 4 times as many candies as Anke. How many candies does Anke have?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Here;
Let Anke = A and Conrad = C
Therefore;
A = C - 5 (since Anke has 5 candies fewer than Conard)
and 4(A - 5) = C + 5 (Since Anke gives Conrad 5 candies, Conrad will then have 4 times as many candies as Anke)
or 4A - 20 = C + 5
or 4A - 20 = A + 5 + 5 (since A = C - 5)
or 3A = 30
or A =10 i.e. Anke have 10 candies
Re: Anke has 5 fewer candies than Conrad. If Anke gives Conrad 5
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05 Jul 2018, 03:10
05 Jul 2018, 03:10
Expert Reply
Explanation
First, translate the problem into two equations, writing “Anke after she gave Conrad 5 candies” as (A – 5) and “Conrad after receiving 5 more candies” as (C + 5):
\(A = C - 5\)
\(4(A - 5) = C + 5\)
Since A = C – 5, plug C – 5 in for A in the second equation:
\(4(C - 5 - 5) = C + 5\)
\(4(C - 10) = C + 5\)
\(4C - 40 = C + 5\)
\(4C = C + 45\)
\(3C = 45\)
\(C = 15\)
If C = 15, then, since Anke has 5 fewer candies, she has A = 10.
Check the answer. If Anke starts with 10 candies, after giving 5 to Conrad she has 5. If Conrad starts with 15 candies, he has 20 after receiving 5 from Anke. It is true that 20 is 4 times 5.
First, translate the problem into two equations, writing “Anke after she gave Conrad 5 candies” as (A – 5) and “Conrad after receiving 5 more candies” as (C + 5):
\(A = C - 5\)
\(4(A - 5) = C + 5\)
Since A = C – 5, plug C – 5 in for A in the second equation:
\(4(C - 5 - 5) = C + 5\)
\(4(C - 10) = C + 5\)
\(4C - 40 = C + 5\)
\(4C = C + 45\)
\(3C = 45\)
\(C = 15\)
If C = 15, then, since Anke has 5 fewer candies, she has A = 10.
Check the answer. If Anke starts with 10 candies, after giving 5 to Conrad she has 5. If Conrad starts with 15 candies, he has 20 after receiving 5 from Anke. It is true that 20 is 4 times 5.
